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Simplifying -2[x + -1(3 + 2) + -3(k + 1)] = 14 + 2k Combine like terms: 3 + 2 = 5 -2[x + -1(5) + -3(k + 1)] = 14 + 2k Multiply -1 * 5 -2[x + -5 + -3(k + 1)] = 14 + 2k Reorder the terms: -2[x + -5 + -3(1 + k)] = 14 + 2k -2[x + -5 + (1 * -3 + k * -3)] = 14 + 2k -2[x + -5 + (-3 + -3k)] = 14 + 2k Reorder the terms: -2[-5 + -3 + -3k + x] = 14 + 2k Combine like terms: -5 + -3 = -8 -2[-8 + -3k + x] = 14 + 2k [-8 * -2 + -3k * -2 + x * -2] = 14 + 2k [16 + 6k + -2x] = 14 + 2k Solving 16 + 6k + -2x = 14 + 2k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2k' to each side of the equation. 16 + 6k + -2k + -2x = 14 + 2k + -2k Combine like terms: 6k + -2k = 4k 16 + 4k + -2x = 14 + 2k + -2k Combine like terms: 2k + -2k = 0 16 + 4k + -2x = 14 + 0 16 + 4k + -2x = 14 Add '-16' to each side of the equation. 16 + 4k + -16 + -2x = 14 + -16 Reorder the terms: 16 + -16 + 4k + -2x = 14 + -16 Combine like terms: 16 + -16 = 0 0 + 4k + -2x = 14 + -16 4k + -2x = 14 + -16 Combine like terms: 14 + -16 = -2 4k + -2x = -2 Add '2x' to each side of the equation. 4k + -2x + 2x = -2 + 2x Combine like terms: -2x + 2x = 0 4k + 0 = -2 + 2x 4k = -2 + 2x Divide each side by '4'. k = -0.5 + 0.5x Simplifying k = -0.5 + 0.5x
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